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Computing Equilibrium Wealth Distributions in Models with Heterogeneous-Agents, Incomplete Markets and Idiosyncratic Risk

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  • Muffasir Badshah

    ()
    (Department of Finance and Economcis, Qatar University, Doha Qatar)

  • Paul Beaumont

    ()
    (Department of Economics, Florida State University)

  • Anuj Srivastava

    ()
    (Department of Statistics, Florida State University)

Abstract

This paper describes an accurate, fast and robust fixed point method for computing the stationary wealth distributions in macroeconomic models with a continuum of infinitely-lived households who face idiosyncratic shocks with aggregate certainty. The household wealth evolution is modeled as a mixture Markov process and the stationary wealth distributions are obtained using eigen structures of transition matrices by enforcing the conditions for the Perron-Frobenius theorem by adding a perturbation constant to the Markov transition matrix. This step is utilized repeatedly within a binary search algorithm to find the equilibrium state of the system. The algorithm suggests an efficient and reliable framework for studying dynamic stochastic general equilibrium models with heterogeneous agents.

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File URL: ftp://econpapers.fsu.edu/RePEc/fsu/wpaper/wp2011_08_02.pdf
File Function: First version, 2011-08
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Bibliographic Info

Paper provided by Department of Economics, Florida State University in its series Working Papers with number wp2011_08_02.

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Length: 24 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:fsu:wpaper:wp2011_08_02

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Keywords: Numerical solutions; Wealth distributions; Stationary equilibria; DSGE models;

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  1. Aiyagari, S Rao, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages 659-84, August.
  2. Michael Reiter, 2006. "Solving heterogeneous-agent models by projection and perturbation," Economics Working Papers 972, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
  4. Lilia Maliar & Fernando Valli & Serguei Maliar, 2009. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm," Working Papers. Serie AD 2009-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
  6. Den Haan, Wouter, 2008. "Comparison of Solutions to the Incomplete Markets Model with Aggregate Uncertainty," CEPR Discussion Papers 7019, C.E.P.R. Discussion Papers.
  7. Aiyagari, S Rao, 1995. "Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1158-75, December.
  8. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  9. Jianjun Miao, 2003. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," Macroeconomics 0310001, EconWPA.
  10. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, September.
  11. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
  12. Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614.
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